Screening and anti-screening of the pairing interaction in low-density neutron matter

We study pairing in low-density neutron matter including the screening interaction due to the exchange of particle-hole and RPA excitations. As bare force we employ the effective low-momentum interaction $V_{low\,k}$, while the Fermi-liquid parameters are taken from a phenomenological energy density functional (SLy4) which correctly reproduces the equation of state of neutron matter. At low density, we find screening, i.e., pairing is reduced, while at higher densities, we find anti-screening, i.e., pairing is enhanced. This enhancement is mostly due to the strongly attractive Landau parameter $f_0$. We discuss in detail the critical temperature $T_c$ in the limit of low densities and show that the suppression of $T_c$ predicted by Gor'kov and Melik-Barkhudarov can only be reproduced if the cutoff of the $V_{low\,k}$ interaction is scaled with the Fermi momentum. We also discuss the effect of non-condensed pairs on the density dependence of $T_c$ in the framework of the Nozi\`eres-Schmitt-Rink theory.